For several decades already, particle colliders have been essential tools for particle physics. From the very beginning, such accelerators have been among the most complicated scientific instruments ever built, including a number of innovative technological developments. Examples are ultrahigh vacuum systems, magnets with a very high magnetic field, and equipment for sub-ns synchronization and sub-mm precision alignment of equipment inside multi-km underground tunnels. Some key technologies are related to the focusing of the beam down to a scale of sub-μm at the collision point to obtain high luminosity. This review provides an overview of collision concepts and technologies for circular particle colliders, starting from the first ideas. In particular, it discusses such novel schemes and related technologies as crab waist collision and round beam collision.